模糊单纯形

Fuzzy Simplex

建立模糊单纯形的概念,证明了它的表示定理,即用简单的方法把模糊单纯形表示成由通常单纯形组成的分解式。

Let X be a n-dimensional real linear space, and the fuzzy setA∈F(X) with supp.A={x∈eX |μA(x)>0}={x0,x1,……,xm},(m≤n), such that{x1-x0=x0,x2-x0,……,xm-x0} is linearly independent in X, then the fuzzysimplex is defined as the fuzzy convex hull of A, i. e., the smallest convex fuzzy act which includes A. The following representation theorem is proved. A fuzzy set △∈F(X) is a fuzzy simplex in X, if and only if there exist real numbers a0,a1, ……,am(1≤α0≤α2≤……≤αm) and ordinary simplices △0,△1,…… ,△m in X such thatWhereαr△f is a fuzzy set with membership function, ,being the characteristic function of △f.